At the bottom of the Inbox page there are options to download all your PMs in one of several formats:
I've tried only the "Text" format so far, but it's worked well enough for me that I haven't even looked at the others. I use Windows XP so the downloaded file opens in Windows Notepad. I get to save it to wherever I want, which for me is a folder called Psych Central > PM Saves. I work the date of the save (yymmdd) into the filename when I save it, so I can distinguish older saves from newer ones. Once I'm sure I've saved my PMs (and backed up the files to CD or something), I can delete any of the originals that I don't expect to need.
When I want to search for a particular PM, I open the file of saved PMs in Notepad and use the "Find" (Ctrl-F) function to search for a username or a distinctive word in the PM.